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Lets say i have a large survey dataset which i want to use as a source for income reporting of the population, e.g. parameters of the distribution, poverty and inequality.

Due to item nonresponse on income, i want to know whether listwise deletion biases my parameters.

Therefore i impute the income variable with a reasonable model (about 50 to 60 percent R2 in the OLS of available cases) applying predictive mean matching as is popular in social sciences, and treat the imputed as "better" data, comparing parameters with listwise deletion.

After that, to assess accuracy of my imputations i simulate missing data by

  1. Estimate a Nonresponse Model by logistic regression and generate the missing probability
  2. Keep all cases without any missings
  3. Set income missing for all cases with probability of missing higher than a certain value
  4. Impute
  5. Compare parameters based in imputed or listwise deletion with original parameters

Although i got a fairly reasonable model with 60% R2, the bias of listwise deletion is not greater on all parameters than by usage of the imputed data. The parameters are the mean, percentiles, poverty indices like at-rate-of-poverty, FGT, as well as inequality like Gini, percentile-ratios, Atkinson, Entropy.

What is the conclusion of that? Is the data at hand to impute the income not sufficient?

I tried using alternate Imputation algorithms, Imputation Models, Transformations of the income variable. I can not seem to get imputation always "win" over listwise deletion. If iam not able to, my conclusion would be not to use imputed values solemnly but rather see the imputed data as sensitivity test for the listwise deletion parameters. If the difference is small, no worries, if its large, then one should be wary of possible bias?

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